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Numerical Technologies for Investigating Optimal Control Problems with Free Right-Hand End of Trajectories

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Advanced Computational Methods for Knowledge Engineering (ICCSAMA 2019)

Part of the book series: Advances in Intelligent Systems and Computing ((AISC,volume 1121))

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Abstract

The paper considers numerical approaches for solving optimal control problems with free trajectories at the end of the time interval. A modification of the algorithm of the conjugate gradient for studying the controlled dynamic problem is presented. The proposed technique has been tested by using the test optimal control problems. We describe the results of solving an applied problem of nanophysics. It is considered two cells of a quantum computer which are based on four tunnel-coupled semiconductor quantum dots. The multistage series of computations for investigation of system dependence from changes of the model parameters values are carried out and allowed to demonstrate the effectiveness of the proposed approach.

Supported by Russian Foundation of Basic Research, project number 18-07-00587.

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References

  1. Pontryagin, L.S., Boltyansky, V.G., Gamkrelidze, R.V., Mishchenko, E.V.: The Mathematical Theory of Optimal Processes. Fizmatgiz, Moscow (1961)

    Google Scholar 

  2. Atans, M., Falb, P.: Optimal control. Mechanical Engineering, Moscow (1968)

    Google Scholar 

  3. Krasovsky, N.N.: To the theory of optimal regulation. Autom. Telemech. 18(11), 960–970 (1957)

    Google Scholar 

  4. Gornov, A.Y., Zarodnyuk, T.S., Finkelshtein, E.A., Anikin, A.S.: The method of uniform monotonous approximation of the reachable set border for a controllable system. J. Glob. Optim. 66(1), 53–64 (2016)

    Article  MathSciNet  Google Scholar 

  5. Gamkrelidze, R.V.: Fundamentals of Optimal Control. Publishing house of the Tbilisi University (1977)

    Google Scholar 

  6. Tolstonogov, A.A.: Differential inclusions in a Banach space. Mathematics and its Applications. Kluwer Academic Publishers, Dordrecht (2000)

    Chapter  Google Scholar 

  7. Gornov, A.Y., Zarodnyuk, T.S., Madzhara, T.I., Daneyeva, A.V., Veyalko, I.A.: A collection of test multiextremal optimal control problems. In: Optimization, Simulation, and Control. Springer Optimization and Its Applications, vol. 76, pp. 257–274 (2013)

    MATH  Google Scholar 

  8. Gornov, A.Y., Zarodnyuk, T.S.: The curvilinear search method of global extremum in optimal control problems. Mod. Tech. Syst. Anal. Simul. 3, 19–26 (2009). (in Russian)

    Google Scholar 

  9. Gornov, A.Y., Zarodnyuk, T.S.: Tunneling algorithm for solving nonconvex optimal control problems. In: Optimization, Simulation, and Control. Springer Optimization and Its Applications, vol. 76, pp. 289–299 (2013)

    MATH  Google Scholar 

  10. Zinovieva, A.F., Nenashev, A.V., Koshkarev, A.A., Zarodnyuk, T.S., Gornov, A.Y., Dvurechenskii, A.V.: Quantum gates with spin states in continuous microwave field. Russ. Microelectron. 47(4), 268–278 (2018)

    Article  Google Scholar 

  11. Gornov, A.Y., Dvurechenskii, A.V., Zarodnyuk, T.S., Zinov’eva, A.F., Nenashev, A.V.: Problem of optimal control in the system of semiconductor quantum points. Autom. Remote Control 72(6), 1242–1247 (2011)

    Article  MathSciNet  Google Scholar 

  12. Brent, R.: On the Davidenko-Branin methods for solving simultaneous nonlinear equations. IBM J. Res. Dev. 16, 434–436 (1972)

    Article  MathSciNet  Google Scholar 

  13. Kasbah, A.B., Astolfi, A., Laila, D.S.: A modified Branin method. In: Proceedings of the 17th International Symposium on Mathematical Theory of Networks and Systems, Kyoto, Japan (2006)

    Google Scholar 

  14. Karpenko, A.P.: Population algorithms of global search searching optimization. Review of new and little-known algorithms. Inf. Technol. 7, 1–32 (2012)

    Google Scholar 

  15. Diveev, A.I., Konstantinov, S.V.: Evolutionary algorithms for solving optimal control problem. Bull. Peoples’ Friendsh. Univ. Russ. Ser.: Eng. Stud. 18(2), 254–265 (2017)

    Google Scholar 

  16. Krotov, V.F.: Global Methods in Optimal Control Theory. Marcel Dekker Inc., New York (1996)

    MATH  Google Scholar 

  17. Dykhta, V.A.: Weakly monotone solutions of the Hamilton-Jacobi inequality and optimality conditions with positional controls. Autom. Remote Control 75(5), 829–844 (2014)

    Article  MathSciNet  Google Scholar 

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Author information

Authors and Affiliations

  1. Matrosov Institute for System Dynamics and Control Theory of SB RAS, Irkutsk, Russia

    Tatiana Zarodnyuk, Alexander Gornov, Anton Anikin & Pavel Sorokovikov

Authors
  1. Tatiana Zarodnyuk
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  2. Alexander Gornov
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  3. Anton Anikin
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  4. Pavel Sorokovikov
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Corresponding author

Correspondence to Tatiana Zarodnyuk .

Editor information

Editors and Affiliations

  1. Computer Science and Applications Department LGIPM, University of Lorraine, Metz Cedex 03, France

    Hoai An Le Thi

  2. Computer Science and Applications Department LGIPM, University of Lorraine, Metz Cedex 03, France

    Hoai Minh Le

  3. Laboratory of Mathematics, National Institute for Applied Sciences, Saint-Étienne-du-Rouvray Cedex, France

    Tao Pham Dinh

  4. Department of Information Systems, Wroclaw University of Science and Technology, Wrocław, Poland

    Ngoc Thanh Nguyen

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Zarodnyuk, T., Gornov, A., Anikin, A., Sorokovikov, P. (2020). Numerical Technologies for Investigating Optimal Control Problems with Free Right-Hand End of Trajectories. In: Le Thi, H., Le, H., Pham Dinh, T., Nguyen, N. (eds) Advanced Computational Methods for Knowledge Engineering. ICCSAMA 2019. Advances in Intelligent Systems and Computing, vol 1121. Springer, Cham. https://doi.org/10.1007/978-3-030-38364-0_9

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